Any person added to a Group by import or manual entry will be started in any corresponding active Automated Workflow steps. They will then receive immediate (upon group join) messages that are set up in the Automated Workflow and their timeline will start for the rest of the scheduled messages. The timing is all based on when a person "is added to the group," regardless of how.
If you don't wish for the new person to get a certain message(s), make the steps inactive and keep them that way until that person has passed the schedule to receive them.
To double-check if a message is active, go to the Groups page, click on the specific group in question, and then click on the Automated Workflows tab.
Now you can see all of the steps in your workflow.
Any step with a green dot is active and ready to send. If it has a red dot, it is inactive and will not send.
To learn more on options to change the status of Automated Workflow messages: